The interpretation of the dual problem also provides an economic interpretation of what
the simplex method does in the primal problem. The goal of the simplex method is to
find how to use the available resources in the most profitable feasible way. To attain
this goal, we must reach a BF solution that satisfies all the requirements on profitable
use of the resources (the constraints of the dual problem). These requirements comprise
the condition for optimality for the algorithm. For any given BF solution, the
requirements (dual constraints) associated with the basic variables are automatically
satisfied (with equality). However, those associated with nonbasic variables may or
may not be satisfied.
In particular, if an original variable xj is nonbasic so that activity j is not used, then
the current contribution to profit of the resources that would be required to undertake each
unit of activity j